Mind if I give the readers who’ve taken an electrostatics class something to noodle over?
Consider a cubic box consisting of six sides of which five are held at a uniform potential of 0 volts. The top side is held at a uniform 100 volts. What is the potential at the center of the cube?
Here’s a hint: The hard way is pretty hard. There is an easy way, and it’s very easy.
It’s a classic example of one of the most important principles in physics – laziness. Ok, that’s a joke. What it’s actually an example of is the idea that sometimes the formally general mathematics obscures the important parts of the problem, which in this case happens to be the fact that the symmetry of this problem itself contains enough information to give us the potential at the center. Knowing how to see those fundamentals can both save you time and allow you to understand the entire problem more cleanly.